The invention relates to an apparatus for the measurement of the mass of a flowing medium. An apparatus is already known for the measurement of the mass of a flowing medium in which a film resistor placed upon a carrier is used as the temperature-dependent resistor. In its application, the apparatus is also used in a Reynolds-number range in which a very unstable, laminar flow predominates. Laminar flow separations appear continuously in this situation which vary the heat-transfer coefficient and thus the measurement signal of the apparatus. However, a sharply fluctuating measurement signal is unsuitable for control purposes.